Subgroups — #25114831

Order 11008.

1022 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14582941	C₂	1	2	yes	maximal, complemented
2	#19137544	C₂	1	1	yes	maximal, characteristic
3	D₄×C₄⋊Dic₄₃	C₂	1	1	yes	maximal, characteristic
4	#19135359	C₂	1	1	yes	maximal, characteristic, complemented
5	#19135354	C₂	1	1	yes	maximal, characteristic, complemented
6	#19134796	C₂	1	2	yes	maximal, complemented
7	#19134785	C₂	1	2	yes	maximal, complemented
8	#19134755	C₂	1	1	yes	maximal, characteristic, complemented
9	#19134628	C₂	1	2	yes	maximal, complemented
10	C₄×#13063257	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₄₃×#436	C₂	1	1	yes	maximal, characteristic
12	C₂×D₄×Dic₄₃	—	2	1	no	—
13	C₂×#13063284	C₂²	1	2	yes	—
14	C₂²×C₄⋊Dic₄₃	C₂²	1	2	yes	—
15	#14582941	—	2	8	no	—
16	C₂×#13063259	C₂²	1	2	yes	—
17	C₂×#13063259	C₂²	1	2	yes	—
18	C₂×#13063259	C₂²	1	2	yes	—
19	C₂×#13063257	C₂²	1	2	yes	—
20	C₂×#13063257	C₂²	1	1	yes	characteristic
21	C₂×#13063257	C₂²	1	1	yes	characteristic
22	#14582802	—	2	1	no	—
23	#14582798	—	2	1	no	—
24	#14582792	—	2	2	no	—
25	#14582774	—	2	2	no	—
26	#14582769	C₂²	1	1	yes	characteristic
27	#14582769	C₂²	1	1	yes	characteristic
28	#14582759	C₂²	1	2	yes	—
29	#14582759	C₂²	1	2	yes	—
30	C₄⋊C₄×Dic₄₃	—	2	1	no	—
31	C₄×C₄⋊Dic₄₃	C₂²	1	1	yes	characteristic
32	C₄×C₄⋊Dic₄₃	C₂²	1	1	yes	characteristic
33	#14582662	C₂²	1	1	yes	characteristic
34	#14582662	C₂²	1	1	yes	characteristic
35	#14582662	C₂²	1	2	yes	—
36	#14582662	C₂²	1	2	yes	—
37	C₂²×M₁₆×C₄₃	C₂²	1	2	yes	—
38	C₂×C₄×D₄×C₄₃	C₂²	1	1	yes	characteristic
39	C₄₃×#436	C₄	1	8	yes	complemented
40	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
41	C₂×C₂²⋊C₈×C₄₃	C₂²	1	2	yes	—
42	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
43	C₂³×Dic₄₃	—	2	2	no	—
44	D₄×Dic₄₃	—	4	4	no	—
45	#13063284	—	2	4	no	—
46	#13063284	—	4	2	no	—
47	C₂×C₄⋊Dic₄₃	—	2	4	no	—
48	C₂×C₄⋊Dic₄₃	—	2	2	no	—
49	C₂×C₄⋊Dic₄₃	—	2	1	no	—
50	C₂×C₄⋊Dic₄₃	—	2	1	no	—
51	C₂×C₄⋊Dic₄₃	—	2	1	no	—
52	C₂×C₄⋊Dic₄₃	—	2	1	no	—
53	C₂×C₄⋊Dic₄₃	—	4	2	no	—
54	C₂×C₄⋊Dic₄₃	C₂³	1	2	yes	—
55	C₂×C₄⋊Dic₄₃	C₂³	1	2	yes	—
56	C₂×C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
57	C₂×C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
58	C₂×C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
59	C₂×C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
60	C₂×C₂²⋊Dic₄₃	—	2	2	no	—
61	C₂×C₂²⋊Dic₄₃	—	2	2	no	—
62	C₂×C₂²⋊Dic₄₃	—	2	2	no	—
63	C₂×C₄×Dic₄₃	—	2	2	no	—
64	C₂×C₄×Dic₄₃	—	2	1	no	—
65	C₂×C₄×Dic₄₃	—	2	1	no	—
66	#13063259	—	2	4	no	—
67	#13063259	—	2	4	no	—
68	#13063259	—	4	2	no	—
69	#13063257	—	2	2	no	—
70	#13063257	—	2	4	no	—
71	#13063257	D₄	1	4	yes	complemented
72	C₄₃⋊#95	—	2	1	no	—
73	C₄₃⋊#95	—	2	2	no	—
74	C₄₃⋊#95	—	2	2	no	—
75	C₄₃⋊#95	—	2	1	no	—
76	C₂²×D₄×C₄₃	D₄	1	1	yes	characteristic
77	C₂³×C₄×C₄₃	C₂³	1	2	yes	—
78	C₂×M₁₆×C₄₃	—	2	4	no	—
79	C₂×M₁₆×C₄₃	—	2	4	no	—
80	C₂×M₁₆×C₄₃	C₂×C₄	1	8	yes	complemented
81	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
82	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
83	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
84	C₄×D₄×C₄₃	C₂×C₄	1	4	yes	—
85	C₄×D₄×C₄₃	Q₈	1	4	yes	—
86	C₂×C₄⋊C₄×C₄₃	D₄	1	1	yes	characteristic
87	C₂×C₂²⋊C₄×C₄₃	D₄	1	2	yes	—
88	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
89	C₄⋊C₈×C₄₃	C₂×C₄	1	4	yes	complemented
90	C₂²⋊C₈×C₄₃	C₂×C₄	1	8	yes	complemented
91	C₄×C₈×C₄₃	C₂×C₄	1	4	yes	complemented
92	C₂⁴×C₄₃	C₂×D₄	1	2	yes	—
93	C₂×D₄×C₄₃	—	2	2	no	—
94	C₂×D₄×C₄₃	—	2	2	no	—
95	C₂×D₄×C₄₃	C₄⋊C₄	1	4	yes	—
96	C₂²×C₄×C₄₃	—	2	2	no	—
97	C₂²×C₄×C₄₃	—	2	2	no	—
98	C₂²×C₄×C₄₃	—	2	2	no	—
99	C₂²×C₄×C₄₃	—	2	2	no	—
100	C₂²×C₄×C₄₃	C₂²×C₄	1	4	yes	—
101	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
102	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
103	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₄₃	C₂×Q₈	1	4	yes	—
105	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
106	C₂²×Dic₄₃	—	2	1	no	—
107	C₂²×Dic₄₃	—	2	1	no	—
108	C₂²×Dic₄₃	—	2	1	no	—
109	C₂²×Dic₄₃	—	2	1	no	—
110	C₂²×Dic₄₃	—	2	2	no	—
111	C₂²×Dic₄₃	—	2	2	no	—
112	C₂²×Dic₄₃	—	4	4	no	—
113	C₂²×Dic₄₃	—	4	4	no	—
114	C₂²×Dic₄₃	—	8	2	no	—
115	M₁₆×C₄₃	—	2	16	no	—
116	C₂×C₈×C₄₃	—	2	2	no	—
117	C₂×C₈×C₄₃	—	2	2	no	—
118	C₂×C₈×C₄₃	—	2	1	no	—
119	C₂×C₈×C₄₃	—	2	1	no	—
120	C₂×C₈×C₄₃	C₂²×C₄	1	2	yes	—
121	C₂×C₈×C₄₃	C₂²×C₄	1	4	yes	—
122	C₂×C₈×C₄₃	C₂²×C₄	1	2	yes	—
123	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
124	C₂×C₈×C₄₃	#41	1	2	yes	—
125	C₄⋊C₄×C₄₃	C₄⋊C₄	1	4	yes	—
126	C₂²⋊C₄×C₄₃	C₄⋊C₄	1	8	yes	—
127	C₄²×C₄₃	C₂²×C₄	1	2	yes	—
128	C₄²×C₄₃	C₂×Q₈	1	2	yes	—
129	C₂²⋊Dic₄₃	—	4	4	no	—
130	C₂²⋊Dic₄₃	—	4	4	no	—
131	C₂²⋊Dic₄₃	—	8	2	no	—
132	C₄⋊Dic₄₃	—	2	1	no	—
133	C₄⋊Dic₄₃	—	2	1	no	—
134	C₄⋊Dic₄₃	—	2	2	no	—
135	C₄⋊Dic₄₃	—	2	2	no	—
136	C₄⋊Dic₄₃	—	2	1	no	—
137	C₄⋊Dic₄₃	—	2	1	no	—
138	C₄⋊Dic₄₃	—	2	2	no	—
139	C₄⋊Dic₄₃	—	2	2	no	—
140	C₄⋊Dic₄₃	—	2	1	no	—
141	C₄⋊Dic₄₃	—	2	1	no	—
142	C₄⋊Dic₄₃	—	4	4	no	—
143	C₄⋊Dic₄₃	—	4	2	no	—
144	C₄⋊Dic₄₃	—	4	2	no	—
145	C₄⋊Dic₄₃	—	8	1	no	—
146	C₄⋊Dic₄₃	—	8	1	no	—
147	C₄⋊Dic₄₃	C₂×D₄	1	2	yes	—
148	C₄⋊Dic₄₃	C₂×D₄	1	2	yes	—
149	C₄×Dic₄₃	—	4	4	no	—
150	C₄×Dic₄₃	—	4	2	no	—
151	C₄×Dic₄₃	—	4	2	no	—
152	C₂³×C₄₃	—	2	2	no	—
153	C₂³×C₄₃	—	2	2	no	—
154	C₂³×C₄₃	—	2	2	no	—
155	C₂³×C₄₃	—	2	2	no	—
156	C₂³×C₄₃	—	2	2	no	—
157	C₂³×C₄₃	—	2	2	no	—
158	C₂³×C₄₃	C₂×C₄⋊C₄	1	4	yes	—
159	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
160	D₄×C₄₃	—	2	8	no	—
161	C₂×C₄×C₄₃	—	2	2	no	—
162	C₂×C₄×C₄₃	—	2	2	no	—
163	C₂×C₄×C₄₃	—	2	1	no	—
164	C₂×C₄×C₄₃	—	2	1	no	—
165	C₂×C₄×C₄₃	—	2	4	no	—
166	C₂×C₄×C₄₃	—	2	4	no	—
167	C₂×C₄×C₄₃	—	2	4	no	—
168	C₂×C₄×C₄₃	—	2	4	no	—
169	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	2	yes	—
170	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	4	yes	—
171	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	2	yes	—
172	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	2	yes	—
173	C₂×C₄×C₄₃	#137	1	2	yes	—
174	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
175	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
176	C₂×C₄×C₄₃	C₂²×Q₈	1	1	yes	characteristic
177	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
178	C₂×C₄×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
179	C₂×C₄×C₄₃	2₋¹⁺⁴	1	1	yes	characteristic
180	C₂×Dic₄₃	—	2	2	no	—
181	C₂×Dic₄₃	—	2	2	no	—
182	C₂×Dic₄₃	—	4	1	no	—
183	C₂×Dic₄₃	—	4	1	no	—
184	C₂×Dic₄₃	—	4	1	no	—
185	C₂×Dic₄₃	—	4	1	no	—
186	C₂×Dic₄₃	—	4	2	no	—
187	C₂×Dic₄₃	—	4	2	no	—
188	C₂×Dic₄₃	—	4	1	no	—
189	C₂×Dic₄₃	—	4	1	no	—
190	C₂×Dic₄₃	—	4	1	no	—
191	C₂×Dic₄₃	—	4	2	no	—
192	C₂×Dic₄₃	—	4	2	no	—
193	C₂×Dic₄₃	—	4	1	no	—
194	C₂×Dic₄₃	—	4	2	no	—
195	C₂×Dic₄₃	—	4	2	no	—
196	C₂×Dic₄₃	—	4	1	no	—
197	C₂×Dic₄₃	—	4	1	no	—
198	C₂×Dic₄₃	—	8	8	no	—
199	C₈×C₄₃	—	2	4	no	—
200	C₈×C₄₃	—	2	2	no	—
201	C₈×C₄₃	C₄×D₄	1	4	yes	complemented
202	#22665	—	43	1	no	maximal, Sylow
203	C₂²×C₄₃	—	2	4	no	—
204	C₂²×C₄₃	—	2	4	no	—
205	C₂²×C₄₃	—	2	4	no	—
206	C₂²×C₄₃	—	4	2	no	—
207	C₂²×C₄₃	—	4	2	no	—
208	C₂²×C₄₃	—	4	2	no	—
209	C₂²×C₄₃	—	4	2	no	—
210	C₂²×C₄₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
211	C₂²×C₄₃	D₄²	1	1	yes	characteristic
212	C₂²×C₄₃	#547	1	1	yes	characteristic
213	C₂²×C₄₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
214	C₂²×C₄₃	C₂×#137	1	1	yes	characteristic
215	C₂²×C₄₃	#576	1	1	yes	characteristic
216	C₂²×C₄₃	#578	1	1	yes	characteristic
217	C₄×C₄₃	—	2	4	no	—
218	C₄×C₄₃	—	2	2	no	—
219	C₄×C₄₃	#428	1	4	yes	complemented
220	C₄×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
221	C₄×C₄₃	#520	1	1	yes	characteristic
222	C₄×C₄₃	D₄×Q₈	1	1	yes	characteristic
223	C₄×C₄₃	#554	1	1	yes	characteristic
224	Dic₄₃	—	4	2	no	—
225	Dic₄₃	—	4	2	no	—
226	Dic₄₃	—	8	1	no	—
227	Dic₄₃	—	8	1	no	—
228	Dic₄₃	—	8	2	no	—
229	Dic₄₃	—	8	2	no	—
230	C₂×#436	D₄₃	1	1	yes	characteristic
231	C₂×#428	—	43	2	no	—
232	#2354	—	43	1	no	—
233	D₄×C₄⋊C₄	—	43	1	no	—
234	#1948	—	43	1	no	—
235	#1947	—	43	1	no	—
236	#1854	—	43	2	no	—
237	#1852	—	43	2	no	—
238	#1845	—	43	1	no	—
239	#1809	—	43	2	no	—
240	C₄×#106	—	43	1	no	—
241	C₂×C₄₃	—	4	4	no	—
242	C₂×C₄₃	D₄×C₄⋊C₄	1	1	yes	characteristic
243	C₂×C₄₃	C₂×#428	1	1	yes	characteristic
244	C₂×C₄₃	#2913	1	1	yes	characteristic
245	C₂×C₄₃	#3274	1	1	yes	characteristic
246	C₂×C₄₃	#3276	1	1	yes	characteristic
247	C₂×C₄₃	#3353	1	1	yes	characteristic
248	C₂×C₄₃	#3357	1	1	yes	characteristic
249	C₂²×M₁₆	C₂×D₄₃	1	2	yes	—
250	C₂×C₄×D₄	—	86	1	no	—
251	C₂×C₄×D₄	C₂×D₄₃	1	1	yes	characteristic
252	C₂×#117	—	43	2	no	—
253	C₂²×C₄⋊C₄	—	43	2	no	—
254	#436	Dic₄₃	1	8	yes	complemented
255	#428	—	86	8	no	—
256	C₂×#107	—	43	2	no	—
257	C₂×#107	—	43	2	no	—
258	C₂×#107	—	43	2	no	—
259	C₂×#106	—	43	1	no	—
260	C₂×#106	—	43	1	no	—
261	C₂×#106	—	43	2	no	—
262	C₂×C₄⋊C₈	C₂×D₄₃	1	1	yes	characteristic
263	C₂×C₂²⋊C₈	C₂×D₄₃	1	2	yes	—
264	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
265	#390	—	86	1	no	—
266	#389	—	86	1	no	—
267	#388	—	86	2	no	—
268	#385	—	86	2	no	—
269	#384	—	43	1	no	—
270	#384	—	43	1	no	—
271	#380	—	43	2	no	—
272	#380	—	43	2	no	—
273	C₄×C₄⋊C₄	—	43	1	no	—
274	C₄×C₄⋊C₄	—	43	1	no	—
275	C₄×C₄⋊C₄	—	86	1	no	—
276	#340	—	43	2	no	—
277	#340	—	43	2	no	—
278	#340	—	43	1	no	—
279	#340	—	43	1	no	—
280	C₄₃	#22665	1	1	yes	characteristic, complemented, Sylow
281	C₂²×D₄	D₁₇₂	1	1	yes	characteristic
282	C₂³×C₄	—	86	2	no	—
283	C₂³×C₄	C₂²×D₄₃	1	2	yes	—
284	C₂×M₁₆	—	2	4	no	—
285	C₂×M₁₆	—	2	4	no	—
286	C₂×M₁₆	C₂×Dic₄₃	1	8	yes	complemented
287	C₂²×C₈	C₂²×D₄₃	1	2	yes	—
288	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
289	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
290	C₄×D₄	—	172	4	no	—
291	C₄×D₄	Dic₈₆	1	4	yes	—
292	C₄×D₄	C₂×Dic₄₃	1	4	yes	—
293	#117	—	86	4	no	—
294	#117	—	172	2	no	—
295	C₂×C₄⋊C₄	—	43	1	no	—
296	C₂×C₄⋊C₄	—	43	1	no	—
297	C₂×C₄⋊C₄	—	43	2	no	—
298	C₂×C₄⋊C₄	—	43	2	no	—
299	C₂×C₄⋊C₄	—	43	1	no	—
300	C₂×C₄⋊C₄	—	43	1	no	—
301	C₂×C₄⋊C₄	—	86	4	no	—
302	C₂×C₄⋊C₄	—	86	1	no	—
303	C₂×C₄⋊C₄	—	86	1	no	—
304	C₂×C₄⋊C₄	—	86	2	no	—
305	C₂×C₄⋊C₄	—	86	1	no	—
306	C₂×C₄⋊C₄	—	86	1	no	—
307	C₂×C₄⋊C₄	—	172	2	no	—
308	C₂×C₄⋊C₄	D₁₇₂	1	1	yes	characteristic
309	C₂×C₂²⋊C₄	—	86	2	no	—
310	C₂×C₂²⋊C₄	—	86	2	no	—
311	C₂×C₂²⋊C₄	—	86	2	no	—
312	C₂×C₂²⋊C₄	D₁₇₂	1	2	yes	—
313	C₂×C₄²	—	86	2	no	—
314	C₂×C₄²	—	86	1	no	—
315	C₂×C₄²	—	86	1	no	—
316	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
317	#107	—	86	4	no	—
318	#107	—	86	4	no	—
319	#107	—	172	2	no	—
320	#106	—	43	4	no	—
321	#106	—	86	4	no	—
322	#106	—	86	2	no	—
323	C₄⋊C₈	C₂×Dic₄₃	1	4	yes	complemented
324	C₂²⋊C₈	C₂×Dic₄₃	1	8	yes	complemented
325	C₄×C₈	C₂×Dic₄₃	1	4	yes	complemented
326	#95	—	86	1	no	—
327	#95	—	86	1	no	—
328	#95	—	86	2	no	—
329	#95	—	86	2	no	—
330	C₂⁴	C₂×D₁₇₂	1	2	yes	—
331	C₂×D₄	—	2	2	no	—
332	C₂×D₄	—	2	2	no	—
333	C₂×D₄	C₄⋊Dic₄₃	1	4	yes	—
334	C₂²×C₄	—	2	2	no	—
335	C₂²×C₄	—	2	2	no	—
336	C₂²×C₄	—	2	2	no	—
337	C₂²×C₄	—	2	2	no	—
338	C₂²×C₄	—	86	1	no	—
339	C₂²×C₄	—	86	1	no	—
340	C₂²×C₄	—	86	1	no	—
341	C₂²×C₄	—	86	1	no	—
342	C₂²×C₄	—	86	2	no	—
343	C₂²×C₄	—	86	2	no	—
344	C₂²×C₄	—	344	2	no	—
345	C₂²×C₄	—	172	4	no	—
346	C₂²×C₄	—	172	4	no	—
347	C₂²×C₄	C₂×Dic₈₆	1	4	yes	—
348	C₂²×C₄	C₂×D₁₇₂	1	2	yes	—
349	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
350	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
351	C₂²×C₄	C₂²×Dic₄₃	1	4	yes	—
352	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
353	M₁₆	—	2	16	no	—
354	C₂×C₈	—	2	2	no	—
355	C₂×C₈	—	2	2	no	—
356	C₂×C₈	—	2	1	no	—
357	C₂×C₈	—	2	1	no	—
358	C₂×C₈	D₄×D₄₃	1	2	yes	—
359	C₂×C₈	#10621900	1	2	yes	—
360	C₂×C₈	C₂²×Dic₄₃	1	2	yes	—
361	C₂×C₈	C₂²×Dic₄₃	1	4	yes	—
362	C₂×C₈	C₂²×Dic₄₃	1	2	yes	—
363	C₄⋊C₄	—	43	2	no	—
364	C₄⋊C₄	—	43	2	no	—
365	C₄⋊C₄	—	86	1	no	—
366	C₄⋊C₄	—	86	1	no	—
367	C₄⋊C₄	—	86	2	no	—
368	C₄⋊C₄	—	86	2	no	—
369	C₄⋊C₄	—	86	1	no	—
370	C₄⋊C₄	—	86	1	no	—
371	C₄⋊C₄	—	86	2	no	—
372	C₄⋊C₄	—	86	2	no	—
373	C₄⋊C₄	—	86	1	no	—
374	C₄⋊C₄	—	86	1	no	—
375	C₄⋊C₄	—	344	1	no	—
376	C₄⋊C₄	—	344	1	no	—
377	C₄⋊C₄	—	172	4	no	—
378	C₄⋊C₄	—	172	2	no	—
379	C₄⋊C₄	—	172	2	no	—
380	C₄⋊C₄	C₄⋊Dic₄₃	1	4	yes	—
381	C₂²⋊C₄	—	344	2	no	—
382	C₂²⋊C₄	—	172	4	no	—
383	C₂²⋊C₄	—	172	4	no	—
384	C₂²⋊C₄	C₄⋊Dic₄₃	1	8	yes	—
385	C₄²	—	172	4	no	—
386	C₄²	—	172	2	no	—
387	C₄²	—	172	2	no	—
388	C₄²	C₂×Dic₈₆	1	2	yes	—
389	C₄²	C₂²×Dic₄₃	1	2	yes	—
390	C₂³	—	2	2	no	—
391	C₂³	—	2	2	no	—
392	C₂³	—	2	2	no	—
393	C₂³	—	2	2	no	—
394	C₂³	—	2	2	no	—
395	C₂³	—	2	2	no	—
396	C₂³	C₂×C₄⋊Dic₄₃	1	4	yes	—
397	C₂³	C₂²×D₁₇₂	1	1	yes	characteristic
398	D₄	—	2	8	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	2	1	no	—
401	C₂×C₄	—	2	1	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	2	4	no	—
404	C₂×C₄	—	2	4	no	—
405	C₂×C₄	—	2	4	no	—
406	C₂×C₄	—	2	4	no	—
407	C₂×C₄	—	86	2	no	—
408	C₂×C₄	—	86	2	no	—
409	C₂×C₄	—	344	8	no	—
410	C₂×C₄	—	172	1	no	—
411	C₂×C₄	—	172	1	no	—
412	C₂×C₄	—	172	1	no	—
413	C₂×C₄	—	172	2	no	—
414	C₂×C₄	—	172	2	no	—
415	C₂×C₄	—	172	1	no	—
416	C₂×C₄	—	172	1	no	—
417	C₂×C₄	—	172	2	no	—
418	C₂×C₄	—	172	2	no	—
419	C₂×C₄	—	172	1	no	—
420	C₂×C₄	—	172	2	no	—
421	C₂×C₄	—	172	2	no	—
422	C₂×C₄	—	172	1	no	—
423	C₂×C₄	—	172	1	no	—
424	C₂×C₄	—	172	1	no	—
425	C₂×C₄	—	172	1	no	—
426	C₂×C₄	C₂×C₄⋊Dic₄₃	1	2	yes	—
427	C₂×C₄	C₂×C₄⋊Dic₄₃	1	4	yes	—
428	C₂×C₄	C₂×C₄⋊Dic₄₃	1	2	yes	—
429	C₂×C₄	#13063353	1	2	yes	—
430	C₂×C₄	#13063358	1	2	yes	—
431	C₂×C₄	C₂³×Dic₄₃	1	1	yes	characteristic
432	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
433	C₂×C₄	C₂²×Dic₈₆	1	1	yes	characteristic
434	C₂×C₄	C₂×#10621900	1	1	yes	characteristic
435	C₂×C₄	#13063371	1	1	yes	characteristic
436	C₂×C₄	#13063372	1	1	yes	characteristic
437	C₈	—	2	4	no	—
438	C₈	—	2	2	no	—
439	C₈	D₄×Dic₄₃	1	4	yes	complemented
440	C₂²	—	2	4	no	—
441	C₂²	—	2	4	no	—
442	C₂²	—	2	4	no	—
443	C₂²	—	4	2	no	—
444	C₂²	—	4	2	no	—
445	C₂²	—	4	2	no	—
446	C₂²	—	4	2	no	—
447	C₂²	C₂²×C₄⋊Dic₄₃	1	1	yes	characteristic
448	C₂²	D₄×D₁₇₂	1	1	yes	characteristic
449	C₂²	#14583553	1	1	yes	characteristic
450	C₂²	C₂×#13063353	1	1	yes	characteristic
451	C₂²	C₂×#13063358	1	1	yes	characteristic
452	C₂²	#14583704	1	1	yes	characteristic
453	C₂²	#14583716	1	1	yes	characteristic
454	C₄	—	2	2	no	—
455	C₄	—	2	4	no	—
456	C₄	—	344	1	no	—
457	C₄	—	344	1	no	—
458	C₄	—	344	2	no	—
459	C₄	—	344	2	no	—
460	C₄	—	172	2	no	—
461	C₄	—	172	2	no	—
462	C₄	#14582941	1	4	yes	complemented
463	C₄	C₂×D₄×Dic₄₃	1	1	yes	characteristic
464	C₄	#14583382	1	1	yes	characteristic
465	C₄	D₄×Dic₈₆	1	1	yes	characteristic
466	C₄	#14583606	1	1	yes	characteristic
467	C₂	—	4	4	no	—
468	C₂	D₄×C₄⋊Dic₄₃	1	1	yes	characteristic
469	C₂	C₂×#14582941	1	1	yes	characteristic
470	C₂	#19143195	1	1	yes	characteristic
471	C₂	#19146217	1	1	yes	characteristic
472	C₂	#19146243	1	1	yes	characteristic
473	C₂	#19147180	1	1	yes	characteristic
474	C₂	#19147222	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂²×D₁₇₂
commutator	C₂×C₄×C₄₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₃
Fitting	C₂×C₄₃×#436	C₂
socle	C₂³×C₄₃	C₂²×D₄
prime radical	C₂²×D₄×C₄₃	D₄
cosocle	C₂²×C₄×C₄₃	C₂⁴
hypercenter	C₂×#436	D₄₃
hypocenter	C₄₃	#22665
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄×D₄ ◁ C₂×#436

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₂×#14582941	C₂	semidirect
4. #19135359	C₂	semidirect
5. #19135354	C₂	semidirect
6. #19134796	C₂	semidirect
7. #19134785	C₂	semidirect
8. #19134755	C₂	semidirect
9. #19134628	C₂	semidirect
10. C₄×#13063257	C₂	semidirect
39. C₄₃×#436	C₄	semidirect
71. #13063257	D₄	semidirect
80. C₂×M₁₆×C₄₃	C₂×C₄	semidirect
89. C₄⋊C₈×C₄₃	C₂×C₄	semidirect
90. C₂²⋊C₈×C₄₃	C₂×C₄	semidirect
91. C₄×C₈×C₄₃	C₂×C₄	semidirect
201. C₈×C₄₃	C₄×D₄	semidirect
219. C₄×C₄₃	#428	semidirect
254. #436	Dic₄₃	semidirect
280. C₄₃	#22665	semidirect
286. C₂×M₁₆	C₂×Dic₄₃	semidirect
323. C₄⋊C₈	C₂×Dic₄₃	semidirect
324. C₂²⋊C₈	C₂×Dic₄₃	semidirect
325. C₄×C₈	C₂×Dic₄₃	semidirect
439. C₈	D₄×Dic₄₃	semidirect
462. C₄	#14582941	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×#14582941	2
#19137544	2
D₄×C₄⋊Dic₄₃	2
#19135359	2
#19135354	2
#19134796	2
#19134785	2
#19134755	2
#19134628	2
C₄×#13063257	2
C₂×C₄₃×#436	2
#22665	43